{
  "abstract": "We investigate bulk--boundary structures in $\\AdS_4/\\CFT_3$ from the viewpoint of gravity as a broken phase of conformal gauge symmetry. A crucial distinction is made between the Euler and Pontryagin characteristic classes. The gauge-theoretic gravitational action contains an Euler sector, whose total-derivative representation gives a boundary form depending on both intrinsic and extrinsic geometry. This structure is different from the Pontryagin descent to the three-dimensional gravitational Chern--Simons functional, whose metric variation gives the Cotton tensor and underlies the mixed boundary conditions studied by de Haro. We perform a Fefferman--Graham expansion of the Euler boundary form in asymptotically $\\AdS_4$ spacetime. The normalizable coefficient $g_{(3)ij}$ does not contribute linearly to the finite Euler boundary term: its contribution from the cubic extrinsic- curvature sector vanishes by $\\mathrm{Tr}\\,g_{(3)}=0$, while curvature-- extrinsic-curvature terms containing $g_{(3)}$ vanish at the conformal boundary. A direct Codazzi analysis additionally shows that the Cotton tensor appears in the asymptotic mixed curvature but its contribution through the tangential-connection boundary variation vanishes for standard Dirichlet data. This indicates two distinct types of bulk--boundary structure: a global/topological Euler relation and a local Pontryagin--Cotton relation. We distinguish this kinematic Cotton appearance from a finite Cotton boundary response and discuss the implications for holographic reconstruction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27511",
  "author_total": 1,
  "authors": [
    {
      "name": "Takeshi Fukuyama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/30pyz6amdkew1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27511",
  "fulltext_url": null,
  "id": "30pyz6amdkew1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27511",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7223145908",
  "pdf_url": "https://arxiv.org/pdf/2610.27511",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/30pyz6amdkew1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.27511",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27511"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Holographic Reconstruction from Broken Conformal Gauge Symmetry",
  "title_text": "Holographic Reconstruction from Broken Conformal Gauge Symmetry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:04Z",
  "url": "https://research.draconitic.com/paper/30pyz6amdkew1",
  "venue": "arXiv",
  "versions": []
}